Concentration: The Language of Solution Strength
What Exactly is Concentration?
Imagine adding a spoonful of sugar to a cup of tea. The sweetness you taste is directly related to the concentration of the sugar in the tea. In scientific terms, concentration is a measure of the amount of a substance, known as the solute, dissolved in a specific volume of another substance, known as the solvent, to form a solution.
While we could describe this as "grams per litre", chemists prefer using moles because chemicals react in simple whole-number ratios of particles, not masses. A mole is simply a fixed number of particles (atoms, molecules, or ions), specifically 6.02 × 10²³ particles, known as Avogadro's constant[1]. This is why the standard unit for concentration is moles per cubic decimetre, symbolized as mol dm⁻³. A cubic decimetre (dm³) is equal to a litre (L), so you might also see it written as mol/L or M (molar).
The concentration (c) of a solution is calculated using the formula:
$ c = \frac{n}{V} $
Where:
• c = concentration in mol dm⁻³
• n = amount of solute in moles (mol)
• V = volume of the solution in cubic decimetres (dm³)
Calculating Concentration Step-by-Step
Let's break down how to use the formula with a practical example.
Example 1: You dissolve 0.5 moles of sodium chloride (table salt) in enough water to make 2.0 dm³ of solution. What is the concentration?
Using the formula $ c = \frac{n}{V} $:
$ c = \frac{0.5 \text{ mol}}{2.0 \text{ dm³}} = 0.25 \text{ mol dm}^{-3} $
This means the solution has a concentration of 0.25 mol dm⁻³.
Often, you start with the mass of a solid, not the number of moles. In this case, you need an extra step to convert mass to moles using the substance's molar mass[2].
Example 2: What is the concentration of a solution made by dissolving 5.85 g of sodium chloride (NaCl) in 0.5 dm³ of water?
Step 1: Find the molar mass of NaCl. From the periodic table: Na = 23.0 g/mol, Cl = 35.5 g/mol. So, molar mass of NaCl = 23.0 + 35.5 = 58.5 g/mol.
Step 2: Calculate the number of moles (n) of NaCl.
$ n = \frac{\text{mass}}{\text{molar mass}} = \frac{5.85 \text{ g}}{58.5 \text{ g mol}^{-1}} = 0.1 \text{ mol} $
Step 3: Calculate the concentration (c).
$ c = \frac{n}{V} = \frac{0.1 \text{ mol}}{0.5 \text{ dm³}} = 0.2 \text{ mol dm}^{-3} $
A Practical Guide to Preparing a Solution
How would you actually make 1.0 dm³ of a 0.5 mol dm⁻³ solution of copper(II) sulfate (CuSO₄) in a lab? You wouldn't just add the solute to 1.0 dm³ of water. The correct procedure ensures accuracy.
Step 1: Calculate the required mass.
Molar mass of CuSO₄ = 63.5 + 32.1 + (4×16) = 159.6 g/mol.
Moles needed, $ n = c × V = 0.5 \text{ mol dm}^{-3} × 1.0 \text{ dm³} = 0.5 \text{ mol} $.
Mass needed = moles × molar mass = 0.5 mol × 159.6 g/mol = 79.8 g.
Step 2: Dissolve the solute. Weigh out 79.8 g of CuSO₄ and add it to a clean beaker. Add a small amount of water to dissolve it completely.
Step 3: Make up to the mark. Carefully pour the solution from the beaker into a 1.0 dm³ volumetric flask. Rinse the beaker and add the rinsings to the flask. Finally, add more water until the bottom of the meniscus[3] just touches the calibration mark on the flask's neck. This ensures the total volume of the solution is exactly 1.0 dm³.
| Solution Description | Qualitative Term | Quantitative Concentration (mol dm⁻³) |
|---|---|---|
| A small pinch of salt in a large pot of water | Dilute | Very low (e.g., 0.001) |
| Seawater | - | Approx. 0.5 (for NaCl) |
| A typical solution used in a school chemistry experiment | - | 0.1 to 2.0 |
| Concentrated sulfuric acid (as supplied in a lab) | Concentrated | Approx. 18.0 |
Concentration in Action: From Labs to Life
Concentration is not just a number in a textbook; it's a concept with real-world power.
In Medicine: Medications like cough syrups or intravenous drips (IVs) have precisely controlled concentrations. A doctor prescribing a 0.1 mol dm⁻³ saline solution for an IV needs it to be exact. If it's too concentrated, it could damage blood cells; if it's too dilute, it won't be effective. Pharmacists must calculate concentrations accurately to ensure patient safety.
In Cooking: When you follow a recipe, you are controlling concentration. The ratio of sugar to water when making lemonade determines how sweet it is. Baking is a series of chemical reactions; the concentration of baking soda (sodium hydrogen carbonate) in your batter affects how much the cake will rise.
In Environmental Science: Scientists measure the concentration of pollutants in water and air. For example, the concentration of nitrate ions (NO₃⁻) in a river sample tells them about fertilizer runoff from farms. High concentrations can be harmful to aquatic life. By quantifying the problem, they can propose and monitor solutions.
Common Mistakes and Important Questions
Q: Is the volume in the formula the volume of the solvent or the solution?
This is the most common mistake. The volume (V) in the formula $ c = \frac{n}{V} $ is always the final volume of the solution, not the volume of solvent you started with. When you dissolve a solid in a liquid, the total volume can change slightly. This is why we use volumetric flasks, which are calibrated to contain a specific volume of the final solution.
Q: What is the difference between a concentrated solution and a saturated solution?
A concentrated solution has a relatively high amount of solute dissolved, but it's a general, qualitative term. A saturated solution is one where no more solute can dissolve at that particular temperature. A saturated solution is always concentrated, but a concentrated solution is not necessarily saturated. You can have a concentrated solution that could still dissolve more solute.
Q: How do I convert from mol dm⁻³ to g dm⁻³?
This is a simple unit conversion using molar mass. To find the concentration in grams per cubic decimetre (g dm⁻³), multiply the concentration in mol dm⁻³ by the molar mass of the solute in g/mol.
$ \text{Concentration (g dm}^{-3}\text{)} = \text{Concentration (mol dm}^{-3}\text{)} × \text{Molar Mass (g mol}^{-1}\text{)} $
For instance, a 1.0 mol dm⁻³ NaCl solution has a concentration of 1.0 × 58.5 = 58.5 g dm⁻³.
Footnote
[1] Avogadro's constant: A fundamental physical constant, approximately $ 6.02 × 10^{23} $, representing the number of constituent particles (usually atoms or molecules) in one mole of a substance. It is the proportionality factor that relates the number of particles to the amount of substance.
[2] Molar Mass (M): The mass of one mole of a substance, typically expressed in grams per mole (g mol⁻¹). It is numerically equal to the relative atomic or molecular mass in atomic mass units (u).
[3] Meniscus: The curved surface of a liquid in a container. In a narrow tube like a volumetric flask or graduated cylinder, the meniscus is concave (curves downward) for water. The volume is read at the bottom of this curve for accuracy.